A308216 Sum of the largest side lengths of all integer-sided obtuse triangles with perimeter n.
0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 10, 0, 12, 12, 21, 14, 24, 24, 44, 27, 67, 40, 85, 54, 104, 82, 126, 101, 149, 123, 201, 160, 244, 187, 292, 230, 327, 294, 382, 329, 439, 403, 539, 444, 625, 508, 699, 594, 775, 688, 879, 786, 986, 869, 1124, 954, 1244, 1071
Offset: 1
Keywords
Links
- Wikipedia, Integer Triangle
Crossrefs
Cf. A308214.
Programs
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Mathematica
Table[Sum[Sum[(n - i - k) (1 - Sign[Floor[(i^2 + k^2)/(n - i - k)^2]]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
Formula
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((i^2 + k^2)/(n-i-k)^2))) * sign(floor((i+k)/(n-i-k+1))) (n-i-k).